Measurements of Turbulent Stress in Curvilinear Coordinates over Wind-driven Surface Waves

The ocean surface waves and the accompanying generation of turbulence on both sides of the interface play a key role in coupling the air and sea, especially in strongly forced conditions. Although the role of surface waves on the air-sea momentum flux has been the subject of several studies, the current understanding is still insufficient. This incomplete physical understanding of the airflow dynamics impedes further investigations in developing physically based parameterizations for improved weather and sea state predictions. Therefore, in the current study, we focus on detailed quantitative measurements of the turbulence in the airflow above strongly forced wind waves.

We present detailed quantitative measurements taken in the large wind-wave tunnel facility at the Air-Sea Interaction Laboratory of the University of Delaware. Air-side velocity measurements were acquired over wind-generated surface waves through a complex flow visualization apparatus: a combined Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF) system. This flow visualization system, which includes six CCD cameras and multiple lasers, allowed us to acquire high-resolution measurements in the airflow above the waves and down to within the viscous sublayer near the interface. Several wind-wave conditions were studied with different wind speeds, ranging from 0.89 to 16.59 m s^-1. Two-dimensional velocity fields are assessed in a wave-following curvilinear coordinate system such that ensemble and wave-phase averages can be obtained close to the interface. The mean, turbulent, and wave-induced velocity fields are then extracted by means of a linear triple decomposition. Mean and turbulent conservation equations for momentum and kinetic energy are derived in this wave-following coordinate system. Mean, Turbulent, and wave-induced fields are then evaluated in order to examine in detail the role of the surface waves in the air-water momentum and energy fluxes.

In contrast to the turbulent flow over flat solid boundaries, i.e. the law of the wall, the presence of the surface waves leads to wave-phase coherent variations in the bulk flow within the so-called wave boundary layer. For example, data show an increase in the turbulent stress with a separation-induced maximum above the downwind side of the wave. Likewise, at the interface, we observe an along wave variation of the viscous stress. Terms in the momentum conservation equations are evaluated and balanced, with the exception of the non-resolved pressure term. The experimentally resolved two-dimensional turbulent kinetic energy also shows a separation-induced maximum downwind of the wave crests. TKE is compared with results from LES simulations for strongly forced young wind-waves.